CN113364502B - Physical layer secure communication method between multi-antenna equipment - Google Patents

Physical layer secure communication method between multi-antenna equipment Download PDF

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CN113364502B
CN113364502B CN202110512016.0A CN202110512016A CN113364502B CN 113364502 B CN113364502 B CN 113364502B CN 202110512016 A CN202110512016 A CN 202110512016A CN 113364502 B CN113364502 B CN 113364502B
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CN113364502A (en
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刘怡良
苏洲
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Xian Jiaotong University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/16—Implementing security features at a particular protocol layer

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Abstract

The invention discloses a physical layer secure communication method among multi-antenna equipment.A transmitter of confidential equipment generates a pre-coding vector according to first channel state information and generates an artificial noise signal according to the pre-coding vector; the security device receiver calculates to obtain a security signal detection vector according to the first channel state information, detects the security signal according to the security signal detection vector and eliminates the cellular user signal; and the base station receiver calculates to obtain a cellular user signal detection matrix according to the second channel state information, detects the cellular user signal according to the cellular user signal detection matrix, and eliminates the secret signal and the artificial noise signal. The invention injects artificial noise to disturb eavesdroppers when the number of the transmitting antennas is equal to that of the receiving antennas, namely, no null space exists, improves the secret transmission rate, and does not influence a secret device receiver.

Description

Physical layer secure communication method between multi-antenna equipment
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a method for physical layer secure communication among multi-antenna equipment.
Background
With the rapid development of networks, there are various sniffing and stealing means for network information, and the broadcasting characteristics of wireless communication propagation media aggravate the risk of information leakage. The physical layer security utilizes random characteristics in wireless channels, such as noise, interference and fading, to perform confidential transmission of information, has the characteristics of security in information theory and no key requirement, and has now gained wide attention in academia and industry.
The physical layer security technology has a key bottleneck of low secure transmission rate, and the reasons for this are two reasons: 1) The gold frequency band resource is mostly allocated to a cellular network or other special networks, and the physical layer security equipment lacks spectrum resources, so that a high-speed security channel is difficult to establish. 2) The unknown wireless channel state information of the eavesdropping end causes the design optimization based on the physical layer secure communication to lack targets and constraints. For this reason, for 1), the existing physical layer is installed. Full research usually multiplexes cellular spectrum resources to establish a secure channel, but cannot deal with interference caused by spectrum multiplexing. For 2), the existing physical layer security technology generally utilizes null-space artificial noise to interfere an eavesdropper without knowing the channel state information of the eavesdropper, and the null-space artificial noise technology cannot interfere with a channel of a legal user, so that the secret transmission rate is improved.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a method for the physical layer secure communication among multi-antenna equipment, which injects artificial noise to disturb an eavesdropper when the number of transmitting antennas is equal to that of receiving antennas, namely, no null space exists, improves the confidential transmission rate, and does not affect a confidential equipment receiver; in addition, the mutual interference between the security device and the cellular network caused by the spectrum reuse can be eliminated by a low-complexity detection technology.
In order to solve the technical problems, the invention is realized by the following technical scheme:
a method for physical layer secure communication between multi-antenna devices comprises the following steps:
the transmitter of the security equipment generates a pre-coding vector according to the first channel state information and generates an artificial noise signal according to the pre-coding vector;
the security device receiver calculates to obtain a security signal detection vector according to the first channel state information, detects a security signal according to the security signal detection vector and eliminates a cellular user signal;
the base station receiver calculates a cellular user signal detection matrix according to second channel state information, detects the cellular user signal according to the cellular user signal detection matrix, and eliminates the secret signal and the artificial noise signal;
and the transmitter of the security equipment calculates to obtain the security interruption probability according to the precoding vector and the security signal detection vector, calculates to obtain the effective security rate according to the security interruption probability, calculates to obtain the optimal security transmission rate according to the effective security rate, and performs physical layer security coding according to the optimal security transmission rate.
Further, the procedure of generating the precoding vector according to the first channel state information by the secure device transmitter includes:
and the transmitter of the security equipment calculates according to the first channel state information to obtain an auxiliary null space, calculates according to the auxiliary null space to obtain an equivalent channel, and decomposes the characteristic value of the equivalent channel to obtain the precoding vector.
Further, the secret device transmitter calculates to obtain an auxiliary null space according to the first channel state information, which is as follows:
Figure BDA0003060653870000021
in the formula, G 0 Is an auxiliary null space; h 0 ＝[h 1 ,h 2 ,...,h M ]Is channel state information of M cellular users, e.g. h 1 Is the channel state information of the first cellular user; i is N Is an identity matrix with rank N; n is the number of security device transmitter antennas; (.) H Is a conjugate transpose operation.
Further, the eigenvalue decomposition of the equivalent channel is performed to obtain the precoding vector, which specifically includes:
to pair
Figure BDA0003060653870000031
Performing eigenvalue decomposition, namely:
Figure BDA0003060653870000032
H 1 ＝G 0 H
definition of lambda 1 Is composed of
Figure BDA0003060653870000033
Maximum eigenvalue, λ 1 The corresponding characteristic vector is b, and the transmitter of the security equipment uses b as a precoding vector;
in the formula, H 1 Is an equivalent channel; u is a unitary matrix composed of eigenvectors; Λ is a diagonal matrix composed of eigenvalues; eig (.) is a eigenvalue decomposition operation; h is BaoChannel state information between the devices; h 0 And H is the first channel state information.
Further, the generating an artificial noise signal according to the precoding vector includes:
Figure BDA0003060653870000034
h 0 ＝wH
by pairing auxiliary vectors h 0 Singular value decomposition to obtain a zero space matrix G u I.e. by
[U 0 ,S,V 0 ]＝SVD(h 0 )
In the formula of U 0 Is h 0 Left singular matrix of (a); v 0 Is h 0 Right singular matrix of (d); s is a diagonal matrix formed by singular values; SVD (.) is a singular value decomposition operation; v 0 Vector formation h corresponding to medium zero singular value 0 Of the null space matrix G u The transmitter of the security device generates a random signal z and injects it into the null space G u To obtain an artificial noise signal G u z。
Further, the secret device receiver calculates a secret signal detection vector according to the first channel state information, which specifically includes:
Figure BDA0003060653870000035
in the formula, w b Is a secret signal detection vector.
Further, the base station receiver calculates a cellular user signal detection matrix according to the second channel state information, which is as follows:
Figure BDA0003060653870000041
Figure BDA0003060653870000042
in the formula, W b Is a cellular user signal detection matrix; g c ＝[g 1 ,g 2 ,...,g M ]Is uplink channel state information, e.g. g, of M cellular users to the base station 1 Is the uplink channel state information from the first cellular user to the base station;
Figure BDA0003060653870000043
is rank of N b The identity matrix of (1); n is a radical of b Is the number of base station receiver antennas; norm (.) is a column-wise normalization operation on the matrix; (.) -1 Is the matrix inversion operation; the channel state information of the interference channel from the secret equipment transmitter to the base station is defined as a matrix G; g b Is a process variable; g and G c Is referred to as second channel state information.
Further, the security device transmitter calculates a security interruption probability according to the precoding vector and the security signal detection vector, which is specifically as follows:
P out (R s )＝F Z (z)
Figure BDA0003060653870000044
Figure BDA0003060653870000045
Figure BDA0003060653870000046
Figure BDA0003060653870000047
Figure BDA0003060653870000048
Figure BDA0003060653870000049
in the formula, P out (R s ) Is the privacy interruption probability; r s Is the secret transmission rate; c s The security capacity is calculated according to the precoding vector and the security signal detection vector; phi i Means for
Figure BDA00030606538700000410
Middle z i The coefficients of (c); gamma-shaped n Is an N-dimensional vector
Figure BDA0003060653870000051
The nth element of (1); p is the transmit power of the transmitter of the security device, P 1 ,…,P M Is the transmit power of the M cellular devices; sigma e Is the noise power at the eavesdropping end.
Further, the effective secret rate is calculated according to the secret interruption probability, and the optimal secret transmission rate is calculated according to the effective secret rate, which is specifically as follows:
Figure BDA0003060653870000052
in the formula (I), the compound is shown in the specification,
Figure BDA0003060653870000053
is the effective secret rate;
by the pair R s One-dimensional search obtains R that maximizes the effective privacy rate s Said maximum effective secret rate R s Noting the optimal secret transmission rate
Figure BDA0003060653870000054
Further, the physical layer security coding according to the optimal secret transmission rate is as follows:
Figure BDA0003060653870000055
where W is the volume of the physical layer secure coding space, generating a W-dimensional lattice, i.e.:
Figure BDA0003060653870000056
will be provided with
Figure BDA0003060653870000057
Is divided into 2 K Individual cosets, namely:
Figure BDA0003060653870000058
codeword s = { s } for information 1 ,...,s i ,...,s K },s i E {0,1} and coset are mapped one by one to complete lattice coding, namely:
Figure BDA0003060653870000059
use of
Figure BDA00030606538700000510
The mesolattice encoding transmits the security information to the security device receiver.
Compared with the prior art, the invention has at least the following beneficial effects:
(1) The physical layer safety communication between the equipment of the invention reuses the frequency spectrum resource of the cellular network, relieves the problem of shortage of frequency spectrum resource, and simultaneously, the interference caused by frequency spectrum multiplexing can be eliminated by the detection of the confidential equipment receiver and the base station receiver;
(2) The artificial noise technology for equipment-to-equipment communication is provided, artificial noise can be generated under the scene that the number of antennas of a transmitter and a receiver of the security equipment is the same, namely, under the condition of no null space, an eavesdropper is interfered on the basis of not influencing the channel quality of the security equipment, and the security capacity of communication is improved;
(3) The invention provides an encoding technology based on a secret interruption probability, and the secret transmission rate is adjusted on the basis of limiting the constraint of the secret interruption probability. In addition, a physical layer security coding scheme based on one-dimensional search is provided, and the effective secrecy rate is improved.
In summary, based on the cellular network frequency band, the information may be transmitted in a confidential manner between the devices through a physical layer security technology, and interference caused by spectrum reuse may be eliminated through a detection technology, so that the method is safe and effective.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the description below are some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is a flow chart of a method for secure physical layer communication between multiple antenna devices according to the present invention;
FIG. 2 is a design drawing of an artificial noise based precoding;
fig. 3 is a design diagram of security device receiver detection based on precoding vectors.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, as a specific embodiment of the present invention, a method for secure physical layer communication between multiple antenna devices according to the present invention includes the following steps:
step 1: the transmitter of the security equipment generates a pre-coding vector according to the first channel state information and generates an artificial noise signal according to the pre-coding vector.
Referring to fig. 2, specifically, the process of generating a precoding vector by the security device transmitter according to the first channel state information includes three processes of channel estimation, precoding vector generation and artificial noise signal generation.
1) Channel estimation
The whole system includes two N-antenna security device pairs, one security device transmitter and one security device receiver, M cellular users, one base station, and one N-antenna security device e An antenna eavesdropper. The security device pair multiplexes uplink spectrum resources with M cellular users, the channel between the security device transmitter and the device receiver is defined as an N x N matrix H, and the interference channel from the cellular user i e { 1., M } to the security device receiver is defined as an N x 1 vector H i ，H 0 ＝[h 1 ,h 2 ,...,h M ]Is the channel state information for M cellular users. The uplink channel from cellular user i e { 1.,. M } to the base station receiver is defined as N b X 1 vector g i ，G c ＝[g 1 ,g 2 ,...,g M ]Is the uplink channel state information of the M cellular users to the base station receiver. The interference channel from the security device transmitter to the base station receiver is defined as N b Xn matrix G. Through a pilot-based channel estimation technique, a base station may train to obtain g i And G. Also based on the channel estimation technique of the pilot frequency, the receiver of the security device can train to obtain H and H i Wherein g is i G, H and H i Shared throughout the network over a broadcast link. The system also has a channel for an eavesdropper, i.e. a channel N from the transmitter of the security device to the eavesdropper e xN matrix H e And the interference channel N from the cellular user i E {1,. -, M } to the eavesdropper e X 1 vector h ie Both instantaneous information are not available, but H can still be obtained from historical data e And h ie The statistical information of (2). H since the eavesdropper is usually hidden outside the line of sight e And h ie Is defined as a Rayleigh fading channel, i.e. a channel with a large number of fading channels
Figure BDA0003060653870000071
And
Figure BDA0003060653870000072
H 0 and H is the first channel state information; g and G c Is referred to as second channel state information.
2) Precoding vector generation
And the transmitter of the security equipment calculates according to the first channel state information to obtain an auxiliary null space, calculates according to the auxiliary null space to obtain an equivalent channel, and decomposes the characteristic value of the equivalent channel to obtain the precoding vector.
In this embodiment, the transmitter of the security device calculates to obtain the auxiliary null space according to the first channel state information, specifically as follows:
Figure BDA0003060653870000081
in the formula, G 0 Is an auxiliary null space; h 0 ＝[h 1 ,h 2 ,...,h M ]Is channel state information of M cellular users, e.g. h 1 Is the channel state information of the first cellular user; i is N Is an identity matrix with rank N; n is the number of security device transmitter antennas; (.) H Is a conjugate transpose operation.
Performing eigenvalue decomposition on the equivalent channel to obtain the precoding vector, specifically as follows:
for is to
Figure BDA0003060653870000082
Performing eigenvalue decomposition, i.e.：
Figure BDA0003060653870000083
H 1 ＝G 0 H
Definition of lambda 1 Is composed of
Figure BDA0003060653870000084
Maximum eigenvalue, λ 1 The corresponding eigenvector is b, the transmitter of the security device uses b as a precoding vector, and the transmitter of the security device uses b as the precoding vector, so that the diversity gain of the MIMO antenna can be obtained.
In the formula, H 1 Is an equivalent channel; u is a unitary matrix composed of eigenvectors; Λ is a diagonal matrix composed of eigenvalues; eig (.) is a eigenvalue decomposition operation; h is channel state information between the security devices; h 0 And the set of H is the first channel state information.
3) Artificial noise signal generation
Specifically, the generating an artificial noise signal according to the precoding vector includes:
Figure BDA0003060653870000085
h 0 ＝wH
by pairing auxiliary vectors h 0 Singular value decomposition to obtain a zero space matrix G u I.e. by
Figure BDA0003060653870000086
In the formula of U 0 Is h 0 Left singular matrix of (a); v 0 Is h 0 A right singular matrix of (a); s is a diagonal matrix composed of singular values; SVD (.) is a singular value decomposition operation; v 0 Vector corresponding to medium zero singular value constitutes h 0 Of the null space matrix G u The secret device transmitter generating a random signalz and injected into the null space G u To obtain an artificial noise signal G u z。
It can be seen that the secure device receiver is not affected by artifacts, since the wHG u z＝0。
Step 2: and the security device receiver calculates a security signal detection vector according to the first channel state information, detects a security signal according to the security signal detection vector and eliminates a cellular user signal.
Referring to fig. 3, specifically, the secret device receiver calculates a secret signal detection vector according to the first channel state information, and the process includes three processes of mixed signal reception, secret signal detection vector generation, and secret signal detection, which specifically includes the following steps:
1) Mixed signal reception
The mixed signal refers to the mixture of the security signal and the interference signal of M cellular users, and the signal received by the receiver of the security device can be expressed as
y＝Hk+n
Where n is white Gaussian additive noise satisfaction
Figure BDA0003060653870000091
2) Secure signal detection vector generation
The secret signal detection vector needs to complete two processes of secret signal collection and interference elimination on multiple receiving antennas simultaneously. Therefore w b The generation process of (a) is as follows: secure device receiver computing
Figure BDA0003060653870000092
In the formula, w b Is a secret signal detection vector. The signals of the M cellular users can be cancelled because w b H 0 x c =0, where x c Are the signals of M cellular users. Secure device receivers are not affected by artifacts because of w b HG u z =0.w can be collectedThe secret signals on multiple receive antennas obtain diversity gain for MIMO because
Figure BDA0003060653870000093
3) Secure signal detection
The receiver of the security device detects the received signal y through w and simultaneously completes the collection of the security signal on a plurality of receiving antennas and the cellular network interference elimination, and the process can be expressed as
Figure BDA0003060653870000101
Where n is white Gaussian additive noise satisfaction
Figure BDA0003060653870000102
And step 3: and the base station receiver calculates a cellular user signal detection matrix according to the second channel state information, detects the cellular user signal according to the cellular user signal detection matrix, and eliminates the secret signal and the artificial noise signal.
Specifically, the base station receiver calculates to obtain a cellular user signal detection matrix according to the second channel state information, and the process includes three flows of mixed signal reception, cellular user signal detection matrix generation, and cellular signal detection, which specifically includes the following steps:
1) Mixed signal reception
The mixed signal is the interference signal of the security device received by the base station and the signals of M cellular users, and the received signals can be expressed as
Figure BDA0003060653870000103
The channel from cellular user j to the base station is defined as g j The signal of cellular user j is defined as x j And satisfy power constraints
Figure BDA0003060653870000104
n b Is satisfied by Gaussian additive white noise
Figure BDA0003060653870000105
Here, gk is considered to be interference due to spectrum reuse, which needs to be eliminated, and
Figure BDA0003060653870000106
considered as inter-user interference, the base station can handle this by detection techniques.
2) Cellular user signal detection matrix generation
The cellular user signal detection matrix needs to simultaneously complete two functions of multi-user signal detection and interference cancellation caused by spectrum multiplexing, and the generation process of the detection matrix can be expressed as follows:
base station receiver computation
Figure BDA0003060653870000107
Figure BDA0003060653870000108
In the formula, W b Is a cellular user signal detection matrix; g c ＝[g 1 ,g 2 ,...,g M ]Is uplink channel state information, e.g. g, of M cellular users to the base station 1 Is the uplink channel state information from the first cellular user to the base station;
Figure BDA0003060653870000109
is a rank of N b The identity matrix of (1); n is a radical of b Is the number of base station receiver antennas; norm (.) is a column-wise normalization operation on the matrix; (.) -1 Is the matrix inversion operation; the channel state information of the interference channel from the security device transmitter to the base station is defined as a matrix G; g b Is a process variable; g and G c Is referred to as second channel state information.
3) Cellular subscriber signal detection
Base station passing through W b The multi-user signal detection and the interference elimination caused by the spectrum multiplexing are completed as follows
Figure BDA0003060653870000111
Wherein w ib Is W b Row i of (1), n b Is white gaussian additive noise satisfied
Figure BDA0003060653870000112
And 4, step 4: and the transmitter of the security equipment calculates according to the precoding vector and the detection vector of the security signal to obtain a security interruption probability, calculates according to the security interruption probability to obtain an effective security rate, calculates according to the effective security rate to obtain an optimal security transmission rate, and performs physical layer security coding according to the optimal security transmission rate.
Specifically, the secrecy device transmitter calculates a secrecy interruption probability according to the precoding vector and the secrecy signal detection vector, and the process includes a secrecy interruption probability theoretical expression, effective secrecy rate optimization, and physical security coding, which specifically includes:
1) Secret interruption probability theoretical expression
Due to eavesdropping of channel state information H e And h ie Unknown, the secret interruption probability of the precoding is needed to be pushed as the basis for setting the physical layer security code rate. The probability of a privacy disruption may be expressed as
P out (R s )＝F Z (z)
Figure BDA0003060653870000113
Figure BDA0003060653870000114
Figure BDA0003060653870000115
Figure BDA0003060653870000116
Figure BDA0003060653870000121
Figure BDA0003060653870000122
In the formula, P out (R s ) Is the privacy interruption probability; r s Is the secret transmission rate; c s The security capacity is calculated according to the precoding vector and the security signal detection vector; phi (phi) of i Means that
Figure BDA0003060653870000123
Middle z i The coefficient of (a); gamma-shaped n Is an N-dimensional vector
Figure BDA0003060653870000124
The nth element of (1); p is the transmit power of the transmitter of the security device, P 1 ,…,P M Is the transmit power of the M cellular devices; sigma e Is the noise power at the eavesdropping end.
2) Efficient privacy rate optimization
Specifically, the effective secret rate is calculated according to the secret interruption probability, and the optimal secret transmission rate is calculated according to the effective secret rate, which specifically includes:
Figure BDA0003060653870000125
in the formula (I), the compound is shown in the specification,
Figure BDA0003060653870000126
is the effective privacy rate;
by the pair R s One-dimensional search obtains R that maximizes the effective privacy rate s Said R maximizing said effective secret rate s Noting the optimal secret transmission rate
Figure BDA0003060653870000127
3) Physical security coding
As a preferred embodiment of the present invention, R is determined by the golden section method s One-dimensional search obtains R that maximizes the effective privacy rate s 。
Specifically, the physical layer security coding is performed according to the optimal secret transmission rate, which specifically includes:
Figure BDA0003060653870000128
where W is the volume of the physical layer security coding space, generating a W-dimensional lattice, i.e.:
Figure BDA0003060653870000129
will be provided with
Figure BDA00030606538700001210
Is divided into 2 K Individual cosets, namely:
Figure BDA0003060653870000131
codeword s = { s ] of information 1 ,...,s i ,...,s K },s i E {0,1} and coset are mapped one by one to complete lattice coding, namely:
Figure BDA0003060653870000132
use of
Figure BDA0003060653870000133
The mesolattice encoding transmits the security information to the security device receiver.
The invention can improve the secret transmission rate of unit frequency spectrum by means of the frequency spectrum multiplexing and artificial noise technology of the base station, carry out the safe communication between the equipment without secret keys, and eliminate the mutual interference between the secret equipment and the cellular network caused by the frequency spectrum multiplexing by utilizing the low-complexity linear detection.
This embodiment is a physical layer security transmitter between multiple antenna devices:
the transmitter of the security equipment calculates to obtain an auxiliary null space according to the first channel state information;
the transmitter of the security equipment obtains an equivalent channel according to the auxiliary null space calculation;
and the transmitter of the security equipment decomposes the eigenvalue of the equivalent channel to obtain a precoding vector.
And the transmitter of the security equipment performs physical layer security coding according to the optimal security transmission rate to complete the transmission process of the security signal.
In this embodiment, a physical layer security receiver between multiple antenna devices:
the security device receiver calculates to obtain a security signal detection vector according to the first channel state information;
the security device receiver detects the security signal according to the security signal detection vector;
the security device receiver cancels the cellular user signal based on the security signal detection vector.
The embodiment provides a base station receiver:
the base station receiver calculates to obtain a cellular user signal detection matrix according to the second channel state information;
the base station receiver detects the cellular user signal according to the cellular user signal detection matrix;
the base station receiver cancels the secret signals and the artificial noise signals according to the cellular user signal detection matrix.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: those skilled in the art can still make modifications or changes to the embodiments described in the foregoing embodiments, or make equivalent substitutions for some features, within the scope of the disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (1)

1. A method for secure physical layer communication between multiple antenna devices, comprising:
the transmitter of the security equipment generates a pre-coding vector according to the first channel state information and generates an artificial noise signal according to the pre-coding vector;
the security device receiver calculates to obtain a security signal detection vector according to the first channel state information, detects a security signal according to the security signal detection vector, and eliminates a cellular user signal;
the base station receiver calculates a cellular user signal detection matrix according to the second channel state information, detects the cellular user signal according to the cellular user signal detection matrix, and eliminates the secret signal and the artificial noise signal;
the transmitter of the security equipment calculates to obtain a security interruption probability according to the precoding vector and the security signal detection vector, calculates to obtain an effective security rate according to the security interruption probability, calculates to obtain an optimal security transmission rate according to the effective security rate, and performs physical layer security coding according to the optimal security transmission rate;
the process of generating the precoding vector by the security device transmitter according to the first channel state information comprises:
the transmitter of the security equipment calculates according to the first channel state information to obtain an auxiliary null space, calculates according to the auxiliary null space to obtain an equivalent channel, and decomposes a characteristic value of the equivalent channel to obtain the precoding vector;
the transmitter of the security device calculates to obtain an auxiliary null space according to the first channel state information, which is as follows:
Figure FDA0003817985520000011
in the formula, G 0 Is an auxiliary null space; h 0 ＝[h 1 ,h 2 ,...,h M ]Is the channel state information of the M cellular users; i is N Is an identity matrix with rank N; n is the number of security device transmitter antennas; (.) H Is a conjugate transpose operation;
performing eigenvalue decomposition on the equivalent channel to obtain the precoding vector, specifically as follows:
for is to
Figure FDA0003817985520000012
And (3) carrying out characteristic value decomposition:
Figure FDA0003817985520000013
H 1 ＝G 0 H
definition of lambda 1 Is composed of
Figure FDA0003817985520000021
Maximum eigenvalue, λ 1 The corresponding characteristic vector is b, and the transmitter of the security device uses b as a precoding vector;
in the formula, H 1 Is an equivalent channel; u is a unitary matrix composed of eigenvectors; Λ is a diagonal matrix composed of eigenvalues; eig (.) is a eigenvalue decomposition operation; h is channel state information between the security devices; h 0 And H is the first channel state information;
generating an artificial noise signal according to the precoding vector specifically as follows:
Figure FDA0003817985520000022
h 0 ＝wH
by pairing auxiliary vectors h 0 Singular value decomposition to obtain a zero space matrix G u ：
[U 0 ,S,V 0 ]＝SVD(h 0 )
In the formula of U 0 Is h 0 Left singular matrix of (a); v 0 Is h 0 Right singular matrix of (d); s is a diagonal matrix formed by singular values; SVD (.) is a singular value decomposition operation; v 0 Vector corresponding to medium zero singular value constitutes h 0 Of the null space matrix G u The transmitter of the security device generates a random signal z and injects it into the null space G u To obtain an artificial noise signal G u z；
The security device receiver calculates a security signal detection vector according to the first channel state information, and the method specifically comprises the following steps:
Figure FDA0003817985520000023
in the formula, w b Is a secret signal detection vector;
the base station receiver calculates a cellular user signal detection matrix according to the second channel state information, and the method specifically comprises the following steps:
Figure FDA0003817985520000024
Figure FDA0003817985520000025
in the formula, W b Is a cellular user signal detection matrix; g c ＝[g 1 ,g 2 ,...,g M ]The uplink channel state information from M cellular users to the base station;
Figure FDA0003817985520000026
is rank of N b The identity matrix of (a); n is a radical of hydrogen b Is the number of base station receiver antennas; norm (.) is a column-wise normalization operation on the matrix; (.) -1 Is the matrix inversion operation; the channel state information of the interference channel from the security device transmitter to the base station is defined as a matrix G; g b Is a process variable; g and G c Referred to as second channel state information;
the security device transmitter calculates a security interruption probability according to the precoding vector and the security signal detection vector, and the method specifically comprises the following steps:
P out (R s )＝F Z (z)
Figure FDA00038179855200000310
Figure FDA0003817985520000031
Figure FDA0003817985520000032
Figure FDA0003817985520000033
Figure FDA0003817985520000034
Figure FDA0003817985520000035
in the formula, P out (R s ) Is the privacy interruption probability; r s Is the secret transmission rate; c s The security capacity is calculated according to the precoding vector and the security signal detection vector; phi i Means that
Figure FDA0003817985520000036
Middle z i The coefficients of (c); gamma-shaped n Is an N-dimensional vector
Figure FDA0003817985520000037
The nth element of (1); p is the transmit power of the transmitter of the security device, P 1 ,…,P M Is the transmit power of the M cellular devices; sigma e Is the noise power of the eavesdropping end;
calculating according to the secret interruption probability to obtain an effective secret rate, and calculating according to the effective secret rate to obtain an optimal secret transmission rate, wherein the effective secret transmission rate is as follows:
Figure FDA0003817985520000038
in the formula (I), the compound is shown in the specification,
Figure FDA0003817985520000039
is the effective privacy rate;
by the pair R s One-dimensional search obtains R that maximizes the effective privacy rate s Said R maximizing said effective secret rate s Noting the optimal secret transmission rate
Figure FDA0003817985520000041
The physical layer security coding according to the optimal secret transmission rate specifically comprises the following steps:
Figure FDA0003817985520000042
wherein, W is the volume of the physical layer security coding space, generating a W-dimensional lattice:
Figure FDA0003817985520000043
will be provided with
Figure FDA0003817985520000044
Is divided into 2 K Each coset:
Figure FDA0003817985520000045
codeword s = { s ] of information 1 ,...,s i ,...,s K },s i E {0,1} and coset mapping one by one to complete lattice coding:
Figure FDA0003817985520000046
use of
Figure FDA0003817985520000047
The mesolattice encoding transmits the security information to the security device receiver.
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